Time delay induced partial death patterns with conjugate coupling in relay oscillators

We investigate the dynamics of delay-coupled relay oscillators with conjugate (or dissimilar) coupling and find the partial death with the phase-flip transition. This phenomenon is quite general and occurs for the limit cycle as well as chaotic relay oscillators. In the regime of partial death, parts of the system oscillate with large amplitude, while other element stays at rest. Using the Stuart-Landau and Rössler oscillators, we demonstrate that partial amplitude death is a robust dynamical state in coupled oscillators. We also studied the mismatch delay and find different types of dynamical pattern with partial death.     

Universal transition to inactivity in global mixed coupling

The collective dynamics of a network of nonlinear oscillators can be represented in terms of activity level of the network. We have studied a universal transition from activity to inactivity in a globally coupled network of identical oscillators. We consider mixed coupling, where some of the network elements interact through the similar variables while others with dissimilar variables. The coupling strength at which the network become inactive is inversely proportional to the fraction of oscillators coupled through dissimilar variables. Results are presented for the network of various globally coupled limit-cycle oscillators such as Stuart-Landau oscillators, MacArthur prey-predator model as well as for the chaotic Rössller oscillators. The analytical condition for the onset of inactivity in the system is calculated using linear stability analysis which is found to be in good agreement with the numerical results.     

Synchronisation in networks of delay-coupled type-I excitable systems

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.     

Mean-field effects on the aging transitions in the damaged networks

We investigate the dynamical robustness property of the damaged network of active and inactive oscillators under the influence of the mean-field diffusion. The tolerance of dynamical activity of the entire coupled network has realized through the aging transition in the coupled dynamical network. We analytically derived the critical threshold of mean-field density and coupling values for the appearance of the aging transition in the damaged network. By using the critical values as a quantifiable measure of dynamical robustness of the damaged network, we showed that higher mean-field value is favorable to increase the dynamical robustness of the entire network. We also perform the numerical experiment on the network of Stuart-Landau oscillators and the obtained numerical results have an excellent agreement with the analytical findings. Finally, we extend our investigation into the coupled time-delayed network and discussed the affirmative influence of the mean-field parameter on the dynamical robustness of the network.     

不同耦合下混沌神经元网络的同步

采用Hindmarsh-Rose神经元动力学模型, 对二维点阵上的神经元网络的同步进行了研究. 为了解不同耦合对网络同步的影响, 提出了一般反馈耦合、分层反馈耦合和分层局域平均场反馈耦合三种方案.研究表明:在耦合强度较小的近邻耦合下, 一般反馈耦合不能使网络达到完全同步, 而分层反馈耦合和分层局域平均场反馈耦合可以使网络出现局部同步和全局同步. 不同形式的耦合会导致网络出现不同的斑图, 随着耦合强度的增大, 网络从不同步到同步的过程也不相同, 一般反馈耦合和分层反馈耦合网络是突然出现全局同步, 同步之前网络出现非周期性的相干斑图; 对于分层局域平均场反馈耦合网络, 同层神经元之间先出现从簇放电同步到同步的转变, 形成靶波, 然后同步区由中心向外逐渐扩大, 最终达到网络的全局同步. 这些结果表明, 只有适当的耦合才能实现信号的无损耗的传递. 此外我们发现分层局域平均场反馈耦合可以促进网络的同步.     

Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics

We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased.     

A new method to construct the integrable coupling system for discrete soliton equation with the Kronecker product

It is shown that the Kronecker product can be applied to construct a new integrable coupling system of discrete soliton equation hierarchy in this Letter. A direct application to the generalized Toda lattice spectral problem leads to a novel integrable coupling system. It is also indicated that the study of integrable couplings by using of the Kronecker product is an efficient and straightforward method.     

Analysis of the power coupling efficiency of the relay mirror system with the transmitter composed of sub-telescope array

Model of the relay mirror system with the transmitter composed of sub-telescope array is established. With this model, the new system is theoretically analyzed in the paper. Power coupling efficiencies of the 3-sub-telescope array system and the common system are calculated. The results show that power coupling efficiency of the system with new configuration is significantly improved in comparison with the common relay mirror system.     

多延时互耦合半导体激光器的实时混沌同步特性

针对双延时和三延时互耦合半导体激光器系统,研究了互耦合延时和互耦合强度对实时混沌同步质量的影响,提出了双延时互耦合系统中可将其中一个互耦合延时看作反馈延时的思想,揭示了多延时互耦合半导体激光器系统实时混沌同步条件和规律.研究结果表明,多延时互耦合系统中,某两条双向链路的互耦合延时比值为2,是实现高品质实时混沌同步的基本条件;增大互耦合强度,可以改善实时混沌同步品质,且在较低的等效耦合强度条件下,双延时互耦合系统较三延时互耦合系统更易于实现良好的实时混沌同步.     

Diffusion-induced inhomogeneity in globally coupled oscillators: swing-by mechanism

It is shown that for random initial conditions, a large population of identical and sufficiently nonisochronous Stuart-Landau oscillators coupled globally and diffusively exhibits inhomogeneity in a resonant way as the diffusive coupling is intensified, where the diffusive coupling constant is real. A category of inhomogeneous (nonsynchronized) solutions is analytically shown to exist, which is either periodic or quasiperiodic.     

多延时互耦合半导体激光器的实时混沌同步特性

针对双延时和三延时互耦合半导体激光器系统,研究了互耦合延时和互耦合强度对实时混沌同步质量的影响,提出了双延时互耦合系统中可将其中一个互耦合延时看作反馈延时的思想,揭示了多延时互耦合半导体激光器系统实时混沌同步条件和规律.研究结果表明,多延时互耦合系统中,某两条双向链路的互耦合延时比值为2,是实现高品质实时混沌同步的基本条件;增大互耦合强度,可以改善实时混沌同步品质,且在较低的等效耦合强度条件下,双延时互耦合系统较三延时互耦合系统更易于实现良好的实时混沌同步.     

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally.     

Non-equilibrium dynamical phases of the two-atom Dicke model

In this paper, we investigate the non-equilibrium dynamical phases of the two-atom Dicke model, which can be realized in a two species Bose–Einstein condensate interacting with a single light mode in an optical cavity. Apart from the usual non-equilibrium normal and inverted phases, a non-equilibrium mixed phase is possible which is a combination of normal and inverted phase. A new kind of dynamical phase transition is predicted from non-superradiant mixed phase to the superradiant phase which can be achieved by tuning the two different atom–photon couplings. We also show that a dynamical phase transition from the non-superradiant mixed phase to the superradiant phase is forbidden for certain values of the two atom–photon coupling strengths.     

Amplitude death in systems of coupled oscillators with distributed-delay coupling

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death.     

A biologically constrained learning mechanism in networks of formal neurons

A new learning mechanism is proposed for networks of formal neurons analogous to Ising spin systems; it brings such models substantially closer to biological data in three respects: first, the learning procedure is applied initially to a network with random connections (which may be similar to a spin-glass system), instead of starting from a system void of any knowledge (as in the Hopfield model); second, the resultant couplings are not symmetrical; third, patterns can be stored without changing the sign of the coupling coefficients. It is shown that the storage capacity of such networks is similar to that of the Hopfield network, and that it is not significantly affected by the restriction of keeping the couplings' signs constant throughout the learning phase. Although this approach does not claim to model the central nervous system, it provides new insight on a frontier area between statistical physics, artificial intelligence, and neurobiology.     

Proton residual dipolar couplings by NMR magnetization exchange in cross-linked elastomers: determination and imaging.

Proton nuclear magnetic resonance (NMR) magnetization exchange is used to investigate residual dipolar couplings in a series of cross-linked poly(styrene-cobutadiene) elastomers. A new model for the dipolar unit is used for the evaluation of the signal decay in magnetization exchange experiments. It takes into account an extended residual dipolar coupling network along the polymer chain. It is shown that in the regime of short mixing times, information about the residual dipolar coupling between methine and methylene protons can be obtained which is not affected by other inter- and intramolecular dipolar couplings. The dynamic order parameter of methine-methylene protons is measured and correlated with cross-link density. This study certifies the quality of a filter for magnetization from residual dipolar couplings which exploit magnetization exchange. The filter can be used to generate contrast in NMR images of heterogeneous elastomers. The first proton NMR parameter image of a dynamic order parameter is presented for a phantom made from poly(styrene-cobutadiene) samples with different cross-link densities.     

Interplay between spin frustration and magnetism in the exactly solved two-leg mixed spin ladder

We study a mixed spin-(3/2,1) ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction.The exactly solved Ising-chain model is employed to investigate the ground-state properties and thermodynamics of the low-dimensional ladder system.Our results show that the competition between different exchange couplings brings in a large variety of ground states characterized by various values of normalized magnetization equal to 0,1/5,2/5,3/5,1.Moreover,an interesting double-peak structure is also detected in the thermal dependence of magnetic susceptibility and specific heat when the frustration comes into play.It is shown that the double-peak phenomenon at zero-field for the case of AF_2 ground-state arises from the very strong antiferromagnetic rung coupling,while other cases are attributed to the excitations induced by temperature and external field around the phase boundary.     

Synchronization in uncertain complex networks

We consider the problem of synchronization in uncertain generic complex networks. For generic complex networks with unknown dynamics of nodes and unknown coupling functions including uniform and nonuniform inner couplings, some simple linear feedback controllers with updated strengths are designed using the well-known LaSalle invariance principle. The state of an uncertain generic complex network can synchronize an arbitrary assigned state of an isolated node of the network. The famous Lorenz system is stimulated as the nodes of the complex networks with different topologies. We found that the star coupled and scale-free networks with nonuniform inner couplings can be in the state of synchronization if only a fraction of nodes are controlled.     

Phase synchronization of bursting neural networks with electrical and delayed dynamic chemical couplings

Diffusive electrical connections in neuronal networks are instantaneous, while excitatoryor inhibitory couplings through chemical synapses contain a transmission time-delay.Moreover, chemical synapses are nonlinear dynamical systems whose behavior can bedescribed by nonlinear differential equations. In this work, neuronal networks withdiffusive electrical couplings and time-delayed dynamic chemical couplings are considered.We investigate the effects of distributed time delays on phase synchronization of burstingneurons. We observe that in both excitatory and Inhibitory chemical connections, the phasesynchronization might be enhanced when time-delay is taken into account. This distributedtime delay can induce a variety of phase-coherent dynamical behaviors. We also study thecollective dynamics of network of bursting neurons. The network model presents theso-called Small-World property, encompassing neurons whose dynamics have two time scales(fast and slow time scales). The neuron parameters in such Small-World network, aresupposed to be slightly different such that, there may be synchronization of the bursting(slow) activity if the coupling strengths are large enough. Bounds for the criticalcoupling strengths to obtain burst synchronization in terms of the network structure aregiven. Our studies show that the network synchronizability is improved, as itsheterogeneity is reduced. The roles of synaptic parameters, more precisely those of thecoupling strengths and the network size are also investigated.     

Quantum correlations dynamics of three-qubit states coupled to an XY spin chain: Role of coupling strengths

We investigate the prominent impacts of coupling strengths on the evolution of entanglement and quantum discord for a three-qubit system coupled to an XY spin-chain environment. In the case of a pure W state, more robust, even larger nonzero quantum correlations can be obtained by tailoring the coupling strengths between the qubits and the environment.For a mixed state consisting of the GHZ and W states, the dynamics of entanglement and quantum discord can characterize the critical point of quantum phase transition. Remarkably, a large nonzero quantum discord is generally retained, while the nonzero entanglement can only be obtained as the system-environment coupling satisfies certain conditions. We also find that the impact of each qubit's coupling strength on the quantum correlation dynamics strongly depends on the variation schemes of the system-environment couplings.